Howdy!
I've owned and shot both the M1 and M1A extensively in the last 20 or so years. I formerly shot military service rifle competition and have the following to say:
The .308 Winchester/7.62 NATO cartridge is inherently more accurate than the .30-06 in service ammunition. The reasons are many, but the shorter case and powder column, and 1-in-12 inch twist rate are two of them. Both can use the same highly developed .30 match quality bullets and powders. Both have great military match quality cases and comparable civilian ammo components available. Both military designs are basically limited to service grade ammunition for velocity, pressure, and bullet weights. Using bullets too heavy or light for the caliber overstresses the actions or reduces reliability. Both use the same quality micrometer rear sight, and both have available "national match" components and accuracy enhancing modifications to make them shoot better.
The M1A with its shorter gas cutoff system gives better accuracy than the long operating rod gas system of the M1. That is not to say that the M1 is not as accurate, it certainly CAN be, but in service grade rifles, the M14 (military M1A) is generally more accurate than a service grade M1. The military chrome plated M1A barrels makes maintenance a breeze. Both rifles should shoot into 1 1/2" to 2" groups at 100 yards using factory ammunition. Accurized rifles will consistently shoot smaller groups than this with quality ammunition.
The en-bloc 8 round clip of the M1 is a pain for changing ammunition or refilling a partial magazine. The 20 round box of the M1A more convenient but heavier and bulkier.
The M1A is slightly shorter (22" barrel and shorter receiver) than the M1 with it's 24" barrel and longer receiver. Weights are fairly close for comparable density wood stocks.
The M1 take down system basically makes accuracy retention more difficult: metal clamps down on wood to secure the action in the stock. The M1A take down system clamps metal down on metal to secure the action in the stock. In match grade rifles, neither action should be routinely taken down.
Cleaning and maintenance tools and accessories are widely available for both. Commercial copies of the M1 and M1A are available, but only the M1 can be 100% original military. M1A receivers are commercially made and assembled with military surplus parts to make complete rifles.
If WWII battle re-enactments are important to you, the M1 wins. If owning and using the last honest-to-god steel and wood service rifle is important to you, the M1A wins. Military match armourers still work on civilian produced M1A rifles, and some outstanding shooters use them.
Either rifle is sure to delight you with it classic lines and old fashioned quality of construction and accuracy. Which one to buy? If affordable 7.62x51 military surplus ammunition is important, the M1A is probably the better choice. If a classic battle rifle made by a WWII or Korean War manufacturer is important, the M1 Garand is.
HTH
John